UNITED NATIONS--The United States said on Monday it was willing to cooperate with Russia, as well as Iran, to try to end the Syrian civil war, but the two big powers clashed over whether to work with Syrian President Bashar al-Assad. Speaking at the annual United Nations General Assembly, U.S. President Barack Obama described Assad as a tyrant and as the chief culprit behind the four-year civil war in which at least 200,000 people have died and millions have been driven from their homes. Russian President Vladimir Putin, in contrast, told the gathering of world leaders that there was no alternative to cooperating with Assad's military in an effort to defeat the Islamic State militant group, which has seized parts of Syria and neighboring Iraq. Putin called for the creation of a broader international antiterrorist coalition with majority-Muslim countries as members, an appeal that may compete with the group that the United States has assembled to fight Islamic State. "The United States is prepared to work with any nation, including Russia and Iran, to resolve the conflict," Obama, who spoke before Putin, told the General Assembly. "But we must recognize that there cannot be, after so much bloodshed, so much carnage, a return to the prewar status quo." The disagreement over Assad raised questions about how Obama and Putin might find common ground during their meeting on the sidelines of the General Assembly. The two leaders began meeting shortly after 5 p.m. Putin walked in first with Obama close behind. Stopping in front of U.S. and Russian flags set up for a photo opportunity, Obama put out his hand and Putin took it for a handshake. With tight-lipped smiles, they did not speak to each other or answer shouted questions from journalists. Later, at a lunch hosted by U.N. Secretary-General Ban Ki-moon, the two men shook hands and clinked glasses. As they did so, Putin smiled but Obama, with a piercing look, did not. Obama did not explicitly call for Assad's ouster and he suggested there could be a "managed transition" away from his rule, the latest sign that despite U.S. animus toward the Syrian leader it was willing to see him stay for some period of time. He dismissed the argument that authoritarianism was the only way to combat groups such as Islamic State, saying: "In accordance with this logic, we should support tyrants like Bashar al-Assad, who drops barrel bombs to massacre innocent children, because the alternative is surely worse." Putin differed, suggesting there was no option but to work with Assad against Islamic State fighters. "We think it is an enormous mistake to refuse to cooperate with the Syrian government and its armed forces who are valiantly fighting terrorism face to face," Putin said during his speech before the U.N. General Assembly. "We should finally acknowledge that no one but President Assad's armed forces and (Kurdish) militia are truly fighting the Islamic State and other terrorist organizations in Syria," he said. French President Francois Hollande and Turkish Prime Minister Ahmet Davutoglu both rejected the possibility of allowing Assad to stay. In voicing a willingness to deal with Iran and Russia, both backers of Assad, Obama was openly acknowledging their influence in Syria and swallowing a somewhat bitter pill for the United States. Tehran has armed the Syrian government and, through its backing of Lebanese Hezbollah fighters, has helped Assad combat rebels seeking to end his family's four-decade rule. Russia has started a military buildup in Syria, where it has a naval base that serves as its foothold in the Middle East. U.S. officials say they believe Putin's buildup of Russian forces, including tanks and warplanes, in Syria mainly reflects Moscow's fear that Assad's grip might be weakening and a desire to shore him up to retain Russian influence in the region. They also see it as a way for Putin to try to project Russian influence more widely, a goal he appeared to achieve on Sunday with Iraq's announcement that Russia, Iran, Syria and the Iraqi government were sharing intelligence on Syria.